I currently have a Intel Core i7-6700 3.4 GHz Quad-Core Processor in my main build (built in 2016) and I'm ready for an upgrade.
Can someone recommend me a new cpu? I'd like something a little beefier and hopefully not have to get a new motherboard (GIGABYTE GA-B150M-DS3H LGA-1151 socket)
The only way to keep the current motherboard is 7700K, but that's reall not worth the upgrade over 6700. You will need a new motherboard. You can get intel 12 and 13th gen or Ryzen 5000 and still use DDR4 RAM, but only if your RAM is at least 3200MHz CL16. If your RAM is slower, then you would've be getting the full potential of the new CPU. And in case you need to buy new RAM, you might as well get DDR5 since it doesn't really cost much more than DDR4, and you can get Ryzen 7000 series CPU.
If you're getting intel 13th gen, make sure you pick the correct motherboard with the right RAM support, while CPUs support both kinds of RAM, the motherboard will only support the one kind it's designed for.